FE Other Disciplines Statics Practice Problems

The current FE Other Disciplines specification assigns 9-14 of the 110 exam questions to Statics. Form A contains 10 original problems in this area. The sample below is published in full, with the same worked-solution format used throughout the book.

A 900 lb load hangs from a ring at joint A. The ring is held by cable AB, which runs upward to the left at $3 5^{\circ}$ above the horizontal, and by cable AC, which runs upward to the right at $5 5^{\circ}$ above the horizontal. The tension in cable AB is most nearly:

(A)516 lb
(B)630 lb
(C)737 lb
(D)785 lb

Show worked solution

Answer: (A)

Cable AB carries 516 lb, the projection of the 900 lb weight onto its own line.

Cable inclinations that sum to $9 0^{\circ}$ make the two cables mutually perpendicular, so the vertical load resolves along each cable line without solving simultaneous equations.

3 5^{\circ} + 5 5^{\circ} = 9 0^{\circ}

Projecting the 900 lb weight onto the AB direction gives that cable's share of the load.

T_{A B} = W sin 3 5^{\circ} = 900 (0.5736) = 516 lb

FE Reference Handbook — Statics: Equilibrium Requirements, Concurrent Force Systems

Why the other choices appear

(B)Uses $900 tan 3 5^{\circ} = 630$ lb, treating the weight as the adjacent side of the angle.
(C)Uses $900 cos 3 5^{\circ} = 737$ lb, which is the tension in cable AC, not AB.
(D)Assumes both cables are inclined at $3 5^{\circ}$ , giving $900/ (2 sin 3 5^{\circ}) = 785$ lb.